Portal de Periódicos da CAPES

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

2021; Multidisciplinary Digital Publishing Institute; Volume: 9; Issue: 16 Linguagem: Inglês

10.3390/math9161932

2227-7390

José Julio Conde Mones, Emmanuel Roberto Estrada Aguayo, José Jacobo Oliveros Oliveros, Carlos Hernández, María Monserrat Morín Castillo,

Image and Signal Denoising Methods

This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.